TL;DR: Has anyone fit a 19x11" rim with a 305/35-19 on a S197 without a minitub? What backspacing? Any pics?

My 2013 GT came with 19X9.5" rear rims and 305/35-19 MT ET Streets. MT recommends at least a 10" rim. On the 9.5s the tires bulge out, I'm seeing uneven wear, and my preferred installer won't mount them on rims under/over the min/max width.

My style of rim isn't sold as 10" rim, but an 11" is available.

If I hadn't just bought a new pair of 305/35 MT ET Streets, I would just sell the whole set.